Optimization of a direct elliptic boundary value problem solver by the combined use of symmetry and Strassen's algorithm

A direct elliptic boundary value problem solver used for meteorological applications has been optimized. The problem to be solved is symmetric under a parity operation, and this is preserved by discretization. Therefore if the mesh possesses this symmetry, then the discretized problem will share this symmetry as well. The direct method can make use of this symmetry on a variable mesh to reduce the cost associated with the slow transform, a matrix product, by half. It is also shown that this can be combined with the Strassen-Winograd algorithm for even better results.